# Populations and Samples

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Populations and Samples
Course 2 7-8 Populations and Samples Do Now Solve. 1. -2N + 20 = 44 2. n/6 – 9 = 16 Hwk: 65

Populations and Samples
Course 2 7-8 Populations and Samples EQ: How do I compare and analyze sampling methods? GPS: M7A2a Given a problem define a variable, write an equation, solve the equation, and interpret the solution.

Populations and Samples
Course 2 7-8 Populations and Samples Vocabulary Population – entire group of objects or individuals considered for a survey Sample – part of a population Random sample – sample in which each individual or object in the entire population has an equal chance of being selected

convenience sample – sample based on members of the population that are readily available.
biased sample – does not fairly represent the population

Samples and Surveys Sampling Method How Members are Chosen Random
Course 3 Samples and Surveys Sampling Method How Members are Chosen Random By chance Systematic According to a rule or formula Stratified At random from randomly chosen subgroups Convenience Easiest to reach Voluntary-response Members choose to be in the sample

Populations and Samples
Course 2 7-8 Populations and Samples In 2002, there were claims that Chronic Wasting Disease (CWD), or Mad Elk Disease, was spreading westward across North America. In order to verify claims such as these, the elk population had to be tested. When information is gathered about a group, such as the elk in North America, the entire group is called the population. Because testing each member of a large group can be difficult or impossible, researchers often study a part of the population, called a sample.

Populations and Samples
Course 2 7-8 Populations and Samples For a random sample, members of the population are chosen at random. This gives every member of the population an equal chance of being chosen. A convenience sample is based on members of the population that are readily available, such as 30 elk in a wildlife preservation area. A random sample is more likely to be representative of a population than a convenience sample is. Helpful Hint

Populations and Samples
Course 2 7-8 Populations and Samples Additional Example 1: Analyzing Sampling Methods Determine which sampling method will better represent the entire population. Justify your answer. Sampling method Maria surveys only the band students she knows personally. Results 84% want blue uniforms Jon writes each band student’s name on a card. He questions those students whose name he draws. 61% want blue uniforms Jon’s sample is a random sample, giving every band member equal chance to be surveyed, so it is the better method.

Populations and Samples
Course 2 7-8 Populations and Samples Check It Out: Example 1 Determine which sampling method will better represent the entire population. Justify your answer. Sampling method Ferdinand surveys every other swimmer on the team. Results 72% want practice early Anna-Maria questions the swimmers who are in her Biology class. 50% want practice early Ferdinand’s sample is a random sample, giving results that better represent the entire swimming team, so it is the better method.

Identify the sampling method used.
Course 3 9-1 Samples and Surveys Additional Example 1A: Identifying Sampling Methods Identify the sampling method used. In a county survey, Democratic Party members whose names begin with the letter D are chosen. systematic The rule is to survey members whose names begin with D.

Identify the sampling method used.
Course 3 9-1 Samples and Surveys Additional Example 1B: Identifying Sampling Methods Identify the sampling method used. A telephone company randomly chooses customers to survey about its service. random Customers are chosen by chance.

Identify the sampling method used.
Course 3 9-1 Samples and Surveys Additional Example 1C: Identifying Sampling Methods Identify the sampling method used. A high school randomly chooses three classes from each grade and then draws three random names from each class to poll about lunch menus. stratified The three classes are the random subgroups. Names are chosen randomly from within the classes.

9-1 Samples and Surveys Check It Out: Example 1A
Course 3 9-1 Samples and Surveys Check It Out: Example 1A Identify the sampling method used. In a county survey, families with 3 or more children are chosen. systematic The rule is to survey families with 3 or more children.

9-1 Samples and Surveys Check It Out: Example 1A
Course 3 9-1 Samples and Surveys Check It Out: Example 1A Identify the sampling method used. In a county survey, families with 3 or more children are chosen. systematic The rule is to survey families with 3 or more children.

9-1 Samples and Surveys Check It Out: Example 1A
Course 3 9-1 Samples and Surveys Check It Out: Example 1A Identify the sampling method used. In a county survey, families with 3 or more children are chosen. systematic The rule is to survey families with 3 or more children.

Populations and Samples
Course 2 7-8 Populations and Samples A biased sample does not fairly represent the population. A study of 50 elk belonging to a breeder could be biased because the breeder’s elk might be less likely to have Mad Elk Disease than elk in the wild.

Populations and Samples
Course 2 7-8 Populations and Samples Additional Example 2: Identifying Potentially Biased Samples Determine whether each sample may be biased. Explain. A. The mayor surveys 100 supporters at a rally about the most important issues to be addressed by the city council. The sample is biased. The supporters may have different ideas than those not at the rally. B. The principal sends out questionnaires to all of the students to find out what kind of music students prefer at dances. The sample is random. The students all have a chance to respond.

Populations and Samples
Course 2 7-8 Populations and Samples Check It Out: Example 2 Determine whether each sample may be biased. Explain. A. The owner of a record shop surveys only customers over the age of 18 who shop at his store. This is not random. Customers under the age of 18 do not have a chance of being chosen. B. The teacher writes the name of each student on a piece of paper and questions the students whose names are drawn. This sampling method is random. Each student has an equal chance of being chosen.

People attending a game
Course 3 Samples and Surveys Check It Out: Example 2C Identify the population and the sample. Give a reason why the sample could be biased. People attending a baseball game were asked if they support the construction of a new stadium in the city. Population Sample Possible Bias People that attend a baseball game are more likely to support the construction of a new stadium. City residents People attending a game

9-1 Samples and Surveys Population Sample Possible Bias
Course 3 9-1 Samples and Surveys Check It Out: Example 2B Identify the population and the sample. Give a reason why the sample could be biased. Eighth-grade students with a 3.0 GPA or higher were polled to determine how long students study each day. Population Sample Possible Bias Eighth grade students Students with 3.0 or higher GPA Students with lower grades are less likely to study as long.

9-1 Samples and Surveys Population Sample Possible Bias
Course 3 9-1 Samples and Surveys Check It Out: Example 2A Identify the population and the sample. Give a reason why the sample could be biased. The first 5 people leaving a movie theater at a sneak preview were asked how they liked the movie. Population Sample Possible Bias People that really enjoy a movie are less likely to be one of the first ones to leave. People that went to the movie The first five people that left

Populations and Samples
Course 2 7-8 Populations and Samples Additional Example 3: Verifying Claims Based on Statistical Data A principal of a school with 1,500 students estimates that about 400 students will attend a band festival on Saturday. A random sample of 25 students showed that 6 of them will attend. Determine whether the principal’s estimate is likely to be accurate. Set up a proportion to predict the total number of students that will attend. Students attending sample # of Students sampled Students attending Student Population =

Populations and Samples
Course 2 7-8 Populations and Samples Additional Example 3 Continued 6 25 x 1500 = 360 = x The estimate is not accurate because the data shows that 360 students are likely to attend.

Populations and Samples
Course 2 7-8 Populations and Samples Check It Out: Example 3 The owner of a large chain restaurant with 1,200 employees estimates that about 250 employees will ask for winter vacation. A random sample of 40 employees showed that 8 of them will ask for the time off. Determine whether the owner’s estimate is likely to be accurate. Set up a proportion to predict the total number of students that will attend. Employees surveyed for time off # of Employees surveyed Employees asking for time off Total # of Employees =

Populations and Samples
Course 2 7-8 Populations and Samples Check It Out: Example 3 Continued 8 40 x 1200 = 240 = x The estimate is accurate because the data shows that 240 employees will ask for time off.

Populations and Samples
Course 2 7-8 Populations and Samples TOTD 1. Determine which sample better represents the entire population. b a. A TV ratings service is surveying residents of Orlando who bought TVs in the last month about their favorite TV show. b. A TV ratings service called residents of Orlando randomly selected from the phone directory to conduct a survey about their favorite show.

Populations and Samples
Course 2 7-8 Populations and Samples TOTD 2. Determine whether each sample may be biased. Explain. a. A convenience store surveys customers one morning to determine what products they may like the store to stock. b. Each student’s name is written on a slip of paper and placed in a box. One slip of paper is selected to determine the student to be the homeroom representative. Biased; at other times of the day, customers may have different preferences. Not biased; the sample is random.

Populations and Samples
Course 2 7-8 Populations and Samples TOTD 3. A local middle school has 2500 students. Morgan interviewed 75 of the students about their library habits. She found that 45 of the students checked out a book weekly. Predict the number of students likely to check out books weekly. 1500